Saturday, January 16, 2016

Banach–Tarski

Ran into this today: pretty clear explanation of a rather complicated paradox.

"Vsauce" doesn't mention that the universe we live in isn't infinitely divisible the way an ideal sphere is, because of Heisenberg Uncertainty. Not just because of our finite understanding of things--the fuzziness is built-in. So in the real world no, you can't divide a sphere into two identical spheres.

Also, I doubt that you can use algorithmic procedures on uncountable sets--that seems like it is built into the definition of countability.